$700 will buy you a car pc and a monitor, if you are careful. You will need to focus on low power, low heat, rugged parts. The Intel Atom boards are a good bet, coupled with a laptop hard-drive and a slim line optical drive. You'll need a DC-DC PSU as well as a shutdown controller so that the pc shuts down gracefully when you turn off the car.
Don't scimp on the monitor. Once everything is in the car, the monitor "is" the carpc. Your best bet is a transreflective unit, and those don't come cheaply. A transreflective Lilliput can run anywhere from $400 to $675, depending on where you get it. I have a standard screen, and I have seen a transreflective. Buy the transreflective, it's worth the price premium.
I've done some legwork for you. You can buy the PC on an egg-like website for around $265 (atom board + ram + optical + hard disk), the monitor for around $400, and a PSU will run somewhere around $70 if you want the startup-shutdown stuff integrated. For a little over $800 with shipping, you have a decent setup. Add $30 - $50 for a gps puck if you want it.
Then you'll need some software. The big two are Roadrunner and Centrafuse. If you're willing to work at it, you can use Roadrunner for free. Centrafuse costs money, but (imo) is easier to get running smoothly. The right one for you is a matter of preference. Add $250 for Centrafuse with navigation.
You'll need to run wire, but you'd be doing that anyway so I didn't include the cost. You can mod the laptop if you want, which will save you some money. Some people on this forum have modded docking stations so that they can remove the laptop easily. Your approach there depends on whether you still need the laptop for use outside the car.
Doing a carpc is not about saving money. It's about having fun with electronics. The main advantage of the PC over other solutions is that it is limitless. You can make the PC do anything that you can dream up.